Related papers: Systematic study of the completeness of two-dimens…
We study the classical mechanics and dynamics of particles that retains some memory of quantum statistics. Our work builds on earlier work on the statistical mechanics and thermodynamics of such particles. Starting from the effective…
In this paper, we give a rigorous proof of the renormalizability of the massive $\phi_4^4$ theory on a half-space, using the renormalization group flow equations. We find that five counter-terms are needed to make the theory finite, namely…
A new non-perturbative approach to quantum field theory --- D-theory --- is proposed, in which continuous classical fields are replaced by discrete quantized variables which undergo dimensional reduction. The 2-d classical O(3) model…
The partition function of 2d conformal field theory is a modular invariant function. It is known that the partition function of a holomorphic CFT whose central charge is a multiple of 24 is a polynomial in the Klein function. In this paper,…
We introduce a technique relying on the use of auxiliary fields in order to eliminate explicit field-derivatives that plague the high orders renormalization group treatment of shift-symmetric, derivative, theories. This technique simplifies…
Starting from the Pauli Hamiltonian operator, we derive a scalar quantum kinetic equations for spin-1/2 systems. Here the regular Wigner two-state matrix is replaced by a scalar distribution function in extended phase space. Apart from…
The new method of multivariate data analysis based on the complements of classical probability distribution to quantum state and Schmidt decomposition is presented. We considered Schmidt formalism application to problems of statistical…
A class of one dimensional classical systems is characterized from an algebraic point of view. The Hamiltonians of these systems are factorized in terms of two functions that together with the Hamiltonian itself close a Poisson algebra.…
The use of classical thermal field to approximate real-time quantum thermal field theory is discussed. For a \lambda\phi^4 theory, it is shown that the classical Rayleigh-Jeans divergence can be canceled with the appropriate counterterms,…
The mechanism of the transition of a dynamical system from quantum to classical mechanics is of continuing interest. Practically it is of importance for the interpretation of multi-particle coincidence measurements performed at macroscopic…
We describe the elements of a novel structural approach to classical field theory, inspired by recent developments in perturbative algebraic quantum field theory. This approach is local and focuses mainly on the observables over field…
In this paper a new functional integral representation for classical dynamics is introduced. It is achieved by rewriting the Liouville picture in terms of bosonic creation-annihilation operators and utilizing the standard derivation of…
This work concerns some issues about the interplay of standard and geometric (Hamiltonian) approaches to finite-dimensional quantum mechanics, formulated in the projective space. Our analysis relies upon the notion and the properties of…
We continue in this paper our program of rederiving all quantum mechanical formalism from the classical one. We now turn our attention to the derivation of the second quantized equations, both for integral and half-integral spins. We then…
We review our recent construction of the $\phi^4$-model on four-dimensional Moyal space. A milestone is the exact solution of the quartic matrix model $Z[E,J]=\int d\Phi \exp(tr(J\Phi- E\Phi^2 -(\lambda/4) \Phi^4))$ in terms of the solution…
The monomer-dimer model is fundamental in statistical mechanics. However, it is $#P$-complete in computation, even for two dimensional problems. A formulation in matrix permanent for the partition function of the monomer-dimer model is…
We use the complex $\phi^4$ field at finite density as a model system for developing further techniques based on worldline formulations of lattice field theories. More specifically we: 1) Discuss new variants of the worm algorithm for…
In classical statistical mechanics, the partition function is defined in phase space. We extend this concept to quantum statistical mechanics using Bohmian trajectories. The quantum partition function in phase space captures the ensemble of…
In this paper we give a novel solution to a classical completion problem for square matrices. This problem was studied by many authors through time, and it is completely solved in [2, 3]. In this paper we relate this classical problem to a…
We show that a semi-classical quantum field theory comes with a versal family with the property that the corresponding partition function generates all path integrals and satisfies a system of 2nd order differential equations determined by…